Problem: Renata moved to her new home a few years ago. Back then, the young oak tree in her back yard was $190$ centimeters tall. She measured it once a year and found that it grew at a constant rate. $3$ years after she moved into the house, the tree was $274$ centimeters tall. How fast did the tree grow?
Explanation: Let's say that the tree grew at a rate of $V$ centimeters per year. Then, the tree grew by $V\cdot T$ centimeters in $T$ years. In addition, we know that when Renata moved to her new home, the tree was $190$ centimeters tall. The tree's height at a given time is found by taking its height when Renata moved to her new home and adding to it the length it grew by since then. We can express this with the equation $H=190+V\cdot T$, where: $H$ represents the tree's height at a given time (in centimeters) $V$ represents the tree's growth rate (in centimeters per year) $T$ represents the time (in years) We know that after $3$ years $(T={3})$, the tree was $274$ centimeters tall $(H={274})$. Let's plug these values into the equation to find the value of $V$. $ \begin{aligned}{274}&=190+V\cdot{3}\\ 3V&=84\\ V&=28\end{aligned}$ Therefore, the tree grew at a rate of $28$ centimeters per year. To find how many years passed until the tree was $344$ centimeters tall, we can plug $H=344$ into the equation and solve for $T$. $ \begin{aligned}344&=190+28T\\ 28T&=154\\ T&=5.5\end{aligned}$ The tree grew at a rate of $28$ centimeters per year. The tree reached a height of $344$ centimeters $5.5$ years after Renata moved into her new home.